![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
This study investigates the heat transfer in metal foams assuming that all the foam cells are cubic. An improved model for the volumetric convective heat transfer coefficient of metal foam was obtained by considering the convective heat transfer and the thermal conduction in the connected foam ligaments. Numerical simulations of a metal foam-filled channel were performed using the local thermal non-equilibrium model to evaluate the model. The theoretical and experimental data agree better with the present model than with other models. The velocity gradient near the metal foam-filled channel wall is greater than in an empty channel, with the wall boundary layer becoming thinner. The temperature differences between the fluid and solid phases are predicted by the model with the pore density affecting the volumetric convective heat transfer coefficient more than the porosity. The volumetric convective heat transfer coefficient significantly increases as the pore density increases. However, the relationship between the volumetric convective heat transfer coefficient and the porosity is not linear. As the porosity increases, the volumetric convective heat transfer coefficient first increases and then decreases. The effect of the solid thermal conductivity on the volumetric convective heat transfer coefficient has an upper limit with a critical value of the solid thermal conductivity for the present conditions.
| Nomenclature | ||
| Acs | = | cross-sectional area of the cylinder, m2 |
| Ah | = | heat transfer area of the cylinder, m2 |
| asf | = | surface area density, m−1 |
| Bi | = | biot number |
| Cf | = | heat capacity of the fluid, J/(kg⋅K) |
| df | = | diameter of the metal foam fibers, m |
| dp | = | pore size, m |
| Dh | = | hydraulic diameter of the channel, m |
| F | = | inertial coefficient, m−1 |
| H | = | channel height, m |
| h | = | convective heat transfer coefficient, W/(m2⋅K) |
| hsf | = | interfacial heat transfer coefficient, W/(m2⋅K) |
| k | = | thermal conductivity, W/(m⋅K) |
| K | = | permeability, m2 |
| l | = | cylinder |
| L | = | channel length, m |
| m | = |
|
| Nu | = | averaged Nusselt number |
| p | = | pressure |
| PPI | = | pores per inch |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| r | = | inner-to-outer diameter ratio |
| u | = | local velocity, m/s |
| q | = | heat flux, W/m2 |
| Q | = | heat transfer rate, W |
| R | = | simplification quantity |
| T | = | temperature, K |
| = | average temperature, K | |
| = | surperficial velocity | |
| V1 | = | cylinder volume, m3 |
| Vc | = | local cell volume, m3 |
| W | = | channel with, m |
| x | = | x-coordinate |
| y | = | y-coordinate |
| z | = | z-coordinate |
| Greek symbols | ||
| θ | = | temperature, θ = T1c − Tf, K |
| ρ | = | density, kg/m3 |
| ρr | = | relative density, kg/m3 |
| μ | = | dynamic viscosity, Pa·s |
| ϵ | = | porosity |
| Φ | = | heat transfer source item |
| Subscripts | ||
| c | = | center |
| d | = | dispersion |
| eff | = | effective |
| s | = | solid |
| se | = | solid effective |
| f | = | fluid |
| fe | = | fluid effective |
| in | = | inlet |
| m | = | mean |
| w | = | wall |
| 1, 2…6 | = | tips of the cylinders |
Acknowledgments
The authors acknowledge financial support for this work from the National Natural Science Foundation of China (No. 51236007).
Additional information
Funding
Notes on contributors
Hui Wang
Hui Wang is a Ph.D. student at the School of Energy and Power Engineering, Xi'an Jiaotong University, under the supervision of Prof. Liejin Guo. She is currently working on the flow and heat transfer characteristics in metal foam media under numerical, theoretical and experimental aspects.
Liejin Guo
Liejin Guo is a professor at the School of Energy and Power Engineering, Xi'an Jiaotong University. He received his Ph.D. degree in thermal engineering from Xi'an Jiaotong University in 1989. He is now the director of the State Key Laboratory of Multiphase Flow in Power Engineering. His main research interests include multiphase flow in petroleum engineering, enhanced heat transfer, hydrogen production by biomass gasification in supercritical water and from solar energy, high-pressure steam-water two-phase flow and boiling heat transfer.